Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.3 Verify Trigonometric Identities - 14.3 Exercises - Problem Solving - Page 929: 39


See below.

Work Step by Step

Using the given identities: $\sec x\tan x-\sin x=\frac{1}{\cos x}\frac{\sin x}{\cos x}-\frac{\sin x\cos^2x}{\cos^2x}=\frac{\sin x}{\cos^2 x}-\frac{\sin x\cos^2x}{\cos^2x}=\frac{\sin x(1-\cos^2 x)}{\cos^2 x}=\frac{\sin^3 x}{\cos^2 x}=\sin x\tan^2 x$ Thus we have shown what we have to.
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